Heat a charcoal grill or a cast-iron skillet over high heat. Spread the cracked peppercorns on a large plate and roll the beef filet in them, coating evenly. Rub the meat with 2 tablespoons of the olive oil or add oil to the skillet. Sear the beef on all sides until well charred, about 2 minutes per side. Refrigerate for 1 to 6 hours.

Peel and quarter the onion. Cut each quarter into 1/2-inch-wide strips. In a salad bowl, toss the onion, 2 tablespoons of the remaining olive oil, 2 tablespoons of the chives, and the balsamic vinegar. Season with salt and pepper to taste. Set aside.

In a separate bowl, toss the arugula leaves with 2 tablespoons of the lemon juice, 2 tablespoons of the remaining olive oil and salt and pepper to taste. Divide the arugula among 4 plates, arranging it in the center of each plate with the wide parts of the leaves facing outward in a spokelike fashion.

Slice the beef crosswise as thin as possible, no more than 1/8-inch thick. Divide the beef slices evenly among the 4 plates, placing them on top of the arugula. Each plate should have 4 to 6 slices, depending on the size of the fillet and thickness of slices. Place a quarter of the onion salad on top of the beef. Drizzle with the remaining olive oil and lemon juice. Sprinkle with the remaining chives, then with kosher salt, about 1/4 teaspoon per plate. Top with the shaved parmesan.